Results 1 to 10 of about 10,388 (168)
Generalizations of Bernoulli numbers and polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a, b) are generalized to the one Bn(x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a, b), and Bn(
Qiu-Ming Luo +3 more
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On Certain Matrices of Bernoulli Numbers [PDF]
Abstract and Applied Analysis, 2014 In this work we compute the determinant and inverse matrices for a certain symmetric matrix of Rayleigh sums. As a special case we also obtain the determinants and inverses for the matrices of the Bernoulli numbers and related numbers.
Ruiming Zhang, Li-Chen Chen
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A note on polyexponential and unipoly Bernoulli polynomials of the second kind
Open Mathematics, 2021 In this paper, the authors study the poly-Bernoulli numbers of the second kind, which are defined by using polyexponential functions introduced by Kims. Also by using unipoly function, we study the unipoly Bernoulli numbers of the second kind, which are ...
Ma Minyoung, Lim Dongkyu
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Bernoulli Numbers and Solitons [PDF]
Journal of Nonlinear Mathematical Physics, 2005 We present a new formula for the Bernoulli numbers as the following integral $$B_{2m} =\frac{(-1)^{m-1}}{2^{2m+1}} \int_{-\infty}^{+\infty} (\frac{d^{m-1}}{dx^{m-1}} {sech}^2 x)^2dx. $$ This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory.
Grosset, Marie-Pierre +1 more
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Advances in Difference Equations, 2021 Recently, Kim et al. (Adv. Differ. Equ. 2020:168, 2020) considered the poly-Bernoulli numbers and polynomials resulting from the moderated version of degenerate polyexponential functions. In this paper, we investigate the degenerate type 2 poly-Bernoulli
Waseem A. Khan +3 more
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Fully degenerate Bernoulli numbers and polynomials
Demonstratio Mathematica, 2022 The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Kim Taekyun, Kim Dae San, Park Jin-Woo
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Several properties of hypergeometric Bernoulli numbers
Journal of Inequalities and Applications, 2019 In this paper, we give several characteristics of hypergeometric Bernoulli numbers, including several identities for hypergeometric Bernoulli numbers which the convergents of the continued fraction expansion of the generating function of the ...
Miho Aoki +2 more
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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
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q-Bernoulli numbers and q-Bernoulli polynomials revisited [PDF]
Advances in Difference Equations, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim Taekyun, Lee Byungje, Ryoo Cheon
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Bernoulli F-polynomials and Fibo–Bernoulli matrices
Advances in Difference Equations, 2019 In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
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